Asymptotic solutions and error estimates for linear systems of difference and differential equations. (Q1427003)

Classical results concerning the asymptotic behavior of solutions of systems of linear differential or difference equations lead to formulae containing factors that are asymptotically constant, i.e., \(k+o(1)\) as \(t\) tends to infinity. The authors are interested in more precise information about the terms \(o(1),\) especially how they depend precisely on certain perturbation terms in the equation. Results along these lines were given by \textit{O. A. Gel'fond} and \textit{I. M. Kubenskaya} [Izv. Akad. Nauk SSSR, Ser. Mat. 17, 83--86 (1953; Zbl 0050.09204)] for scalar difference equations and the authors have extended and generalized one of them as well as provided some corresponding results for differential equations.